Computational Engineering of discrete metamaterials
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The physical realisation of complex structures through additive manufacturing technologies has led to significant interest in computational metamaterials. Predictive computational methods are a key part of modern product systems engineering and are particularly useful when trial-and-error methods (manufacture and test) are not feasible due to resource limitations. Since then, a great deal of research has been conducted into buckling behaviour, inelasticity, grading and multi-lattices [1–3]. The modelling and simulation of these cellular structures has been thoroughly investigated in terms of both periodic and continuous manufacturing. However, these structures have several drawbacks: They cannot be scaled up indefinitely in terms of size, variety of material, shape complexity and functionality integration due to manufacturing constraints. The discretisation of periodic metamaterials, as explored in [4], allows the implementation of heterogeneous structures and materials, as well as complex functionality, which would be impossible to generate even with today's most advanced manufacturing systems. The proposed research work builds on the concept of discrete metamaterials from a computational engineering perspective. The core concept of the discretisation of unit cells (cubic or higher) involves an assembly of monolithic beam elements populating one face (intra-face), as well as an imperfect contact strategy between the joints of the contacting faces (inter-face). The struts that span a face are represented by quadratic hybrid Timoshenko beam elements with circular cross-sections. (Non)-linear material models are integrated and calibrated. Geometric nonlinearity in terms of post-buckling behaviour is investigated using a combination of linear eigenvalue analysis and Riks analysis. The computational pipeline includes parametric design, curvature-adaptive discretisation in CAD and an automated API for preparing the simulation with regard to micro- (beam) and meso- (face) discretisation. It also includes the simulation's execution using commercial structural analysis software. This approach enables the detailed simulation of heterogeneous lattice structures based on discrete metamaterials.
